The field of the invention is medical imaging and particularly, methods for reconstructing images from acquired image data.
Magnetic resonance imaging (MRI) uses the nuclear magnetic resonance (NMR) phenomenon to produce images. When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but process about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B1) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, MZ, may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment Mt. A signal is emitted by the excited spins, and after the excitation signal B1 is terminated, this signal may be received and processed to form an image.
When utilizing these signals to produce images, magnetic field gradients (GX GY and GZ) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. Each measurement is referred to in the art as a “view” and the number of views determines the quality of the image. The resulting set of received NMR signals, or views, or k-space samples, are digitized and processed to reconstruct the image using one of many well known reconstruction techniques. The total scan time is determined in part by the length of each measurement cycle, or “pulse sequence”, and in part by the number of measurement cycles, or views, that are acquired for an image. There are many clinical applications where total scan time for an image of prescribed resolution and SNR is a premium, and as a result, many improvements have been made with this objective in mind.
Projection reconstruction methods have been known since the inception of magnetic resonance imaging and this method is again being used as disclosed in U.S. Pat. No. 6,487,435. Rather than sampling k-space in a rectilinear, or Cartesian, scan pattern as is done in Fourier imaging and shown in FIG. 2A, projection reconstruction methods sample k-space with a series of views that sample radial lines extending outward from the center of k-space as shown in FIG. 2B. The number of views needed to sample k-space determines the length of the scan and if an insufficient number of views are acquired, streak artifacts are produced in the reconstructed image. The technique disclosed in U.S. Pat. No. 6,487,435 reduces such streaking by acquiring successive undersampled images with interleaved views and sharing peripheral k-space data between successive image frames.
In a computed tomography (“CT”) system, an x-ray source projects a fan-shaped beam which is collimated to lie within an X-Y plane of a Cartesian coordinate system, termed the “image plane.” The x-ray beam passes through the object being imaged, such as a medical patient, and impinges upon an array of radiation detectors. The intensity of the transmitted radiation is dependent upon the attenuation of the x-ray beam by the object and each detector produces a separate electrical signal that is a measurement of the beam attenuation. The attenuation measurements from all the detectors are acquired separately to produce what is called the “transmission profile”.
The source and detector array in a conventional CT system are rotated on a gantry within the imaging plane and around the object so that the angle at which the x-ray beam intersects the object constantly changes. The transmission profile from the detector array at a given angle is referred to as a “view” and a “scan” of the object comprises a set of views made at different angular orientations during one revolution of the x-ray source and detector. In a 2D scan, data is processed to construct an image that corresponds to a two dimensional slice taken through the object.
As with MRI, there are a number of clinical applications for x-ray CT where scan time is at a premium. In time-resolved angiography, for example, a series of image frames are acquired as contrast agent flows into the region of interest. Each image is acquired as rapidly as possible to obtain a snapshot that depicts the inflow of contrast. This clinical application is particularly challenging when imaging coronary arteries or other vessels that require cardiac gating to suppress motion artifacts.
There are two methods used to reconstruct images from an acquired set of projection views as described, for example, in U.S. Pat. No. 6,710,686. In MRI the most common method is to regrid the k-space samples from their locations on the radial sampling trajectories to a Cartesian grid. The image is then reconstructed by performing a 2D or 3D Fourier transformation of the regridded k-space samples. The second method for reconstructing an MR image is to transform the radial k-space projection views to Radon space by first Fourier transforming each projection view. An image is reconstructed from these signal projections by filtering and backprojecting them into the field of view (FOV). As is well known in the art, if the acquired signal projections are insufficient in number to satisfy the Nyquist sampling theorem, streak artifacts are produced in the reconstructed image.
The prevailing method for reconstructing an image from 2D x-ray CT data is referred to in the art as the filtered backprojection technique. This backprojection process is essentially the same as that used in MR image reconstruction discussed above and it converts the attenuation signal measurements acquired in the scan into integers called “CT numbers” or “Hounsfield units”, which are used to control the brightness of a corresponding pixel on a display.
The standard backprojection method used in both the MRI and x-ray CT is graphically illustrated in FIG. 3. Each acquired signal projection profile 10 is backprojected onto the field of view 12 by projecting each signal sample 14 in the profile 10 through the FOV 12 along the projection path as indicted by arrows 16. In backprojecting each signal sample 14 into the FOV 12 no a priori knowledge of the subject being imaged is used and the assumption is made that the signals in the FOV 12 are homogeneous and that the signal sample 14 should be distributed equally in each pixel through which the projection path passes. For example, a projection path 8 is illustrated in FIG. 3 for a single signal sample 14 in one signal projection profile 10 as it passes through N pixels in the FOV 12. The signal value (P) of this signal sample 14 is divided up equally between these N pixels:Sn=(P×1)/N  (1)
where: Sn is the signal value distributed to the nth pixel in a projection path having N pixels.
Clearly, the assumption that the backprojected signal in the FOV 12 is homogeneous is not correct. However, as is well known in the art, if certain corrections are made to each signal profile 10 and a sufficient number of profiles are acquired at a corresponding number of projection angles, the errors caused by this faulty assumption are minimized and image artifacts are suppressed. In a typical, filtered backprojection method of image reconstruction, 400 projections are required for a 256×256 pixel 2D image and 203,000 projections are required for a 256×256×256 voxel 3D image.
Recently a new image reconstruction method known in the art as “HYPR” and described in co-pending U.S. patent application Ser. No. 11/482,372, filed on Jul. 7, 2006 and entitled “Highly Constrained Image Reconstruction Method” was disclosed and is incorporated by reference into this application. With the HYPR method a composite image is reconstructed from acquired data to provide a priori knowledge of the subject being imaged. This composite image is then used to highly constrain the image reconstruction process. HYPR may be used in a number of different imaging modalities including magnetic resonance imaging (MRI), x-ray computed tomography (CT), positron emission tomography (PET), single photon emission computed tomography (SPECT) and digital tomosynthesis (DTS).
As shown in FIG. 1, for example, when a series of time-resolved images 2 are acquired in a dynamic study, each image frame 2 may be reconstructed using a very limited set of acquired views. However, each such set of views is interleaved with the views acquired for other image frames 2, and after a number of image frames have been acquired, a sufficient number of different views are available to reconstruct a quality composite image 3 for use according to the HYPR method. A composite image 3 formed by using all the interleaved projections is thus much higher quality, and this higher quality is conveyed to the image frame by using the highly constrained image reconstruction method 4. The image frames 2 may also be acquired in a dynamic study in which the dosage (e.g., x-ray) or exposure time (e.g., PET or SPECT) is reduced for each image frame. In this case the composite image is formed by accumulating or averaging measurements from the series of acquired image frames. The highly constrained reconstruction 4 of each image frame 2 conveys the higher SNR of this composite image to the resulting reconstructed image.
A discovery of the HYPR method is that good quality images can be produced with far fewer projection signal profiles if a priori knowledge of the signal contour in the FOV 12 is used in the reconstruction process. Referring to FIG. 4, for example, the signal contour in the FOV 12 may be known to include structures such as blood vessels 18 and 20. That being the case, when the backprojection path 8 passes through these structures a more accurate distribution of the signal sample 14 in each pixel is achieved by weighting the distribution as a function of the known signal contour at that pixel location. As a result, a majority of the signal sample 14 will be distributed in the example of FIG. 4 at the backprojection pixels that intersect the structures 18 and 20. For a backprojection path 8 having N pixels this highly constrained backprojection may be expressed as follows:
                              S          n                =                              (                          P              ×                              C                n                                      )                    /                                    ∑                              n                =                1                            N                        ⁢                                                  ⁢                          C              n                                                          (        2        )            
where: Sn=the backprojected signal magnitude at a pixel n in an image frame being reconstructed;
P=the signal sample value in the projection profile being backprojected; and
Cn=signal value of an a priori composite image at the nth pixel along the backprojection path. The composite image is reconstructed from data acquired during the scan, and may include that used to reconstruct the image frame as well as other acquired image data that depicts the structure in the field of view.
The numerator in equation (2) weights each pixel using the corresponding signal value in the composite image and the denominator normalizes the value so that all backprojected signal samples reflect the projection sums for the image frame and are not multiplied by the sum of the composite image.
While the normalization can be performed on each pixel separately after the backprojection, in many clinical applications it is far easier to normalize the projection P before the backprojection. In this case, the projection P is normalized by dividing by the corresponding value Pc in a projection through the composite image at the same view angle. The normalized projection P/Pc is then backprojected and the resulting image is then multiplied by the composite image.
A 3D embodiment of the highly constrained backprojection is shown pictorially in FIG. 5 for a single 3D projection view characterized by the view angles θ and φ. This projection view is back projected along axis 16 and spread into a Radon plane 21 at a distance r along the back projection axis 16. Instead of a filtered back projection in which projection signal values are filtered and uniformly distributed into the successive Radon planes, along axis 16, the projection signal values are distributed in the Radon plane 21 using the information in the composite image. The composite image in the example of FIG. 5 contains vessels 18 and 20. The weighted signal contour value is deposited at image location x, y, z in the Radon plane 21 based on the intensity at the corresponding location x, y, z in the composite image. This is a simple multiplication of the backprojected signal profile value P by the corresponding composite image voxel value. This product is then normalized by dividing the product by the projection profile value from the corresponding image space projection profile formed from the composite image. The formula for the 3D reconstruction isI(x,y,z)=Σ(P(r,θ,φ)*C(x,y,z)(r,θ,φ)/Pc(r,θ,φ))  (2a)where the sum (Σ) is over all projections in the image frame being reconstructed and the x, y, z values in a particular Radon plane are calculated using the projection profile value P(r,θ,φ) at the appropriate r,θ,φ value for that plane. Pc(r,θ,φ) is the corresponding projection profile value from the composite image, and C(x,y,z)r,θ,φ is the composite image value at (r,θ,φ).
The HYPR method works well under certain circumstances. First, HYPR works best with “sparse” data sets in which the subject of interest in the field of view occupies a small fraction of the image space. In the limit of extremely sparse images or images with complete spatio-temporal correlation the HYPR reconstruction method provides nearly exact reconstruction. As the sparsity and spatio-temporal correlation deteriorate the accuracy of the HYPR reconstruction decreases and local signals can be altered due to the influence of signals elsewhere in the field of view that have different temporal behavior.